Solution
= Solution
{c}
Take \b[$Y=X_1+X_1'$], where $X_1'$ is an independent copy of $X_1$. The preceding factorization gives $\mathbb Ee^{tY}=M_1(t)^2$. Using $2X_1$ would instead give $M_1(2t)$, so an independent copy is required.
= Solution
{c}
Take \b[$Y=X_1+X_1'$], where $X_1'$ is an independent copy of $X_1$. The preceding factorization gives $\mathbb Ee^{tY}=M_1(t)^2$. Using $2X_1$ would instead give $M_1(2t)$, so an independent copy is required.